I think to answer this question you need to go back to the motives of the boys, and particularly of T., for destroying the house and in particular for burning the money. Consider what T. says before burning the savings of "Old Misery":
"We aren't thieves," T. said. "Nobody's going to steal anything from this house. I kept these for you and me - a celebration." He knelt down on the floor and counted them out. There were seventy in all. "We'll burn them," he said, "one by one," and taking it in turns they held a note upward and lit the top corner, so that the flame burnt slowly toward their fingers. The grey ash floated above them and fell on their heads like age.
Note that T. calls this "something special" and a "celebration." It is well worth us thinking why it is that T. doesn't want to steal the money and keep it, but merely burns it. Since T.'s family income has declined, burning Old Misery's money, rather than stealing it, may seem to T. the ultimate way to show that he finds no value in what the world finds meaningful. T., after all, is obsessed with the destruction of the house, and in burning the money Greene shows us a symbol of his nihilism. The quote you highlighted seems to emphasise how world weary these boys are - how they have grown up with nothing but war and destruction for all of their lives, and are much older than their years.